Diana wins this matchup, you have to accept this. After lvl 6, use Q to farm if necessary and DON'T get hit by her Q. Use Riftwalk only for defense or if jungler is nearby and not for offense, otherwise she'll outrade you.

Diana's spellset and playstyle play completely against Kassadin's; Pale Cascade both blocks damage and wounds him as he jumps in for a trade, and Lunar Rush exceeds Riftwalk's range, leaving him no chance of escape from a bad fight